MATHEMATICS AS A QUASI-EMPIRICAL SCIENCE

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3 Citazioni (Scopus)

Abstract

The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call 'set theory' is not 'one' theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T(1),..., T(n) in which T(i+1) supersedes T(i). This thesis has great philosophical significance because it implies that there is a sense in which mathematical theories, like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of this article consists in arguing that Cantor-Zermelo set theory is a Lakatosian Mathematical Research Programme (MRP).
Lingua originaleEnglish
pagine (da-a)41-79
Numero di pagine39
RivistaFoundations of Science
Volume11
Stato di pubblicazionePublished - 2006

All Science Journal Classification (ASJC) codes

  • General
  • History and Philosophy of Science

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